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Abstract:

Kraichnan's seminal ideas on inverse cascades yielded new tools to study common phenomena in geophysical turbulent flows. In the atmosphere and the oceans, rotation and stratification result in a flow that can be approximated as two-dimensional at very large scales but which requires considering three-dimensional effects to fully describe turbulent transport processes and non-linear phenomena. Motions can thus be classified into two classes: fast modes consisting of inertia-gravity waves and slow quasi-geostrophic modes for which the Coriolis force and horizontal pressure gradients are close to balance. In this paper, we review previous results on the strength of the inverse cascade in rotating and stratified flows and then present new results on the effect of varying the strength of rotation and stratification (measured by the inverse Prandtl ratio N/f, of the Coriolis frequency to the Brunt- Väisäla frequency) on the amplitude of the waves and on the flow quasi-geostrophic behavior. We show that the inverse cascade is more efficient in the range of N/f for which resonant triads do not exist, 1/2 ≤ N/f ≤ 2.We then use the spatio-temporal spectrum to show that in this range slow modes dominate the dynamics, while the strength of the waves (and their relevance in the flow dynamics) is weaker.

Registro:

Documento: Artículo
Título:Inverse cascades and resonant triads in rotating and stratified turbulence
Autor:Oks, D.; Mininni, P.D.; Marino, R.; Pouquet, A.
Filiación:Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Fisica, and IFIBA, CONICET, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Laboratoire de Physique-UMR 5672, Ecole Normale Suṕerieure de Lyon, CNRS, 46 Alĺee d'Italie,, Lyon, 69007, France
NCAR, P.O. Box 3000, Boulder, CO 80307-3000, United States
Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS, École Centrale de Lyon, Université de Lyon, Écully, 69134, France
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309-256, United States
Palabras clave:Astrophysics; Horizontal pressure; Inertia gravity waves; Non-linear phenomena; Quasi-geostrophic; Spatio-temporal spectrum; Stratified turbulence; Three dimensional effect; Turbulent transport process; Rotation
Año:2017
Volumen:29
Número:11
DOI: http://dx.doi.org/10.1063/1.5001740
Título revista:Physics of Fluids
Título revista abreviado:Phys. Fluids
ISSN:10706631
CODEN:PHFLE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v29_n11_p_Oks

Referencias:

  • Kraichnan, R.H., Inertial ranges in two-dimensional turbulence (1967) Phys. Fluids, 10, p. 1417
  • Kraichnan, R.H., Montgomery, D., Two-dimensional turbulence (1980) Rep. Prog. Phys., 43, p. 547
  • Clercx, H.J.H., van Heijst, G.J.F., Energy spectra for decaying 2D turbulence in a bounded domain (2000) Phys. Rev. Lett., 85, p. 306
  • Bracco, A., McWilliams, J.C., Murante, G., Provenzale, A., Weiss, J.B., Revisiting freely decaying two-dimensional turbulence at millennial resolution (2000) Phys. Fluids, 12, p. 2931
  • Kellay, H., Goldburg, W.I., Two-dimensional turbulence: A review of some recent experiments (2002) Rep. Prog. Phys., 65, p. 845
  • Biferale, L., Musacchio, S., Toschi, F., Inverse energy cascade in three-dimensional isotropic turbulence (2012) Phys. Rev. Lett., 108, p. 164501
  • Boffetta, G., Ecke, R.E., Two-dimensional turbulence (2011) Annu. Rev. Fluid Mech., 44, p. 427
  • Mininni, P.D., Pouquet, A., Inverse cascade behavior in freely decaying two-dimensional fluid turbulence (2013) Phys. Rev. E, 87, p. 033002
  • Pouquet, A., On two-dimensional magnetohydrodynamic turbulence (1978) J. Fluid Mech., 88, p. 1
  • Ting, A.C., Matthaeus, W.H., Montgomery, D., Turbulent relaxation processes in magnetohydrodynamics (1986) Phys. Fluids, 29, p. 3261
  • Christensson, M., Hindmarsh, M., Brandenburg, A., Inverse cascade in decaying three-dimensional magnetohydrodynamic turbulence (2001) Phys. Rev. E, 64, p. 056405
  • Mininni, P.D., Montgomery, D.C., Pouquet, A.G., A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows (2005) Phys. Fluids, 17, p. 035112
  • Alexakis, A., Mininni, P.D., Pouquet, A., On the inverse cascade of magnetic helicity (2006) Astrophys. J., 640, p. 335
  • Mininni, P.D., Inverse cascades and α effect at a low magnetic Prandtl number (2007) Phys. Rev. E, 76, p. 026316
  • Demoulin, P., Pariat, E., Modelling and observations of photospheric magnetic helicity (2009) Adv. Space Res., 43, p. 1013
  • Lorenz, E.N., The predictability of a flow which possesses many scales of motion (1969) Tellus, 21, p. 289
  • Leith, C.E., Atmospheric predictability and two-dimensional turbulence (1971) J. Atmos. Sci., 28, p. 145
  • Leith, C.E., Kraichnan, R.H., Predictability of turbulent flows (1972) J. Atmos. Sci., 29, p. 1041
  • Boffetta, G., Musacchio, S., Predictability of the inverse energy cascade in 2D turbulence (2001) Phys. Fluids, 13, p. 1060
  • Charney, J.G., Geostrophic turbulence (1971) J. Atmos. Sci., 28, p. 1087
  • Herring, J.R., The inverse cascade range of quasi-geostrophic turbulence (1988) Meteorol. Atmos. Phys., 38, p. 106
  • Boffetta, G., De Lillo, F., Musacchio, S., Inverse cascade in Charney- Hasegawa-Mima turbulence (2002) Europhys. Lett., 59, p. 687
  • Fox, S., Davidson, P.A., The competition between quadratic and integral invariants in inviscid truncated two-dimensional and quasigeostrophic shallow-water turbulence (2009) Phys. Fluids, 21, p. 125102
  • Vallgren, A., Lindborg, E., Charney isotropy and equipartition in quasigeostrophic turbulence (2010) J. Fluid Mech., 656, p. 448
  • Müller, W.-C., Thiele, M., Scaling and energy transfer in rotating turbulence (2007) Europhys. Lett., 77, p. 34003
  • Davidson, P.A., Turbulence in Rotating Stratified and Electrically Conducting Fluids (2013), (Cambridge University Press, Cambridge, ); Nastrom, G.D., Gage, K.S., Jasperson, W.H., Kinetic energy spectrum of large-and mesoscale atmospheric processes (1984) Nature, 310, p. 36
  • Nastrom, G.D., Gage, K.S., A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft (1985) J. Atmos. Sci., 42, p. 950
  • Sukoriansky, S., Dikovskaya, N., Galperin, B., On the arrest of inverse energy cascade and the Rhines scale (2007) J. Atmos. Sci., 64, p. 3312
  • Scott, R.B., Wang, F., Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry (2005) J. Phys. Oceanogr., 35, p. 1650
  • Schlösser, F., Eden, C., Diagnosing the energy cascade in a model of the North Atlantic (2007) Geophys. Res. Lett., 34
  • Verma, M.K., Variable enstrophy flux and energy spectrum in twodimensional turbulence with Ekman friction (2011) Europhys. Lett., 98, p. 14003
  • Lilly, D.K., Stratified turbulence and the mesoscale variability of the atmosphere (1983) J. Atmos. Sci., 40, p. 749
  • Salmon, R., (1998) Lectures on Geophysical Fluid Dynamics, , (Oxford University Press, New York, )
  • Lindborg, E., The effect of rotation on the mesoscale energy cascade in the free atmosphere (2005) Geophys. Res. Lett., 32
  • Riley, J.J., Lindborg, E., Stratified turbulence:Apossible interpretation of some geophysical turbulence measurements (2008) J. Atmos. Sci., 65, p. 2416
  • Smith, L.M., Waleffe, F., Generation of slow large scales in forced rotating stratified turbulence (2002) J. Fluid Mech., 451, p. 145
  • Laval, J.-P., McWilliams, J.C., Dubrulle, B., Forced stratified turbulence: Successive transitions with Reynolds number (2003) Phys. Rev. E, 68, p. 036308
  • Waite, M.L., Bartello, P., Stratified turbulence dominated by vortical motion (2004) J. Fluid Mech., 517, p. 281
  • Waite, M.L., Bartello, P., The transition from geostrophic to stratified turbulence (2006) J. Fluid Mech., 568, p. 89
  • Sen, A., Mininni, P.D., Rosenberg, D., Pouquet, A., Anisotropy and nonuniversality in scaling laws of the large-scale energy spectrum in rotating turbulence (2012) Phys. Rev. E, 86, p. 036319
  • Rorai, C., Rosenberg, D., Pouquet, A., Mininni, P.D., Helicity dynamics in stratified turbulence in the absence of forcing (2013) Phys. Rev. E, 87, p. 063007
  • Rorai, C., Mininni, P.D., Pouquet, A., Turbulence comes in bursts in stably stratified flows (2014) Phys. Rev. E, 89, p. 043002
  • Polzin, K.L., Lvov, Y.V., Toward regional characterizations of the oceanic internal wavefield (2011) Rev. Geophys., 49
  • Ivey, G.N., Winters, K.B., Koseff, J.R., Density stratification, turbulence, but how much mixing? (2008) Annu. Rev. Fluid Mech., 40, p. 169
  • di Leoni, P.C., Mininni, P.D., Absorption ofwaves by large-scale winds in stratified turbulence (2015) Phys. Rev. E, 91, p. 033015
  • Brethouwer, G., Billant, P., Lindborg, E., Chomaz, J.-M., Scaling analysis and simulation of strongly stratified turbulent flows (2007) J. Fluid Mech., 585, p. 343
  • Lindborg, E., Brethouwer, G., Stratified turbulence forced in rotational and divergent modes (2007) J. Fluid Mech., 586, p. 83
  • Aluie, H., Kurien, S., Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows (2011) Europhys. Lett., 96, p. 44006
  • Waite, M.L., Stratified turbulence at the buoyancy scale (2011) Phys. Fluids, 23, p. 066602
  • Almalkie, S., de Bruyn Kops, S.M., Kinetic energy dynamics in forced, homogeneous, and axisymmetric stably stratified turbulence (2012) J. Turbul., 13, p. N29
  • Kimura, Y., Herring, J.R., Energy spectra of stably stratified turbulence (2012) J. Fluid Mech., 698, p. 19
  • Barker, A.J., Lithwick, Y., Non-linear evolution of the tidal elliptical instability in gaseous planets and stars (2013) Mon. Not. R. Astron. Soc., 435, p. 3614
  • Reun, T.L., Favier, B., Barker, A., Bars, M.L., Inertial wave turbulence driven by elliptical instability (2017) Phys. Rev. Lett., 119, p. 034502
  • Bartello, P., Geostrophic adjustment and inverse cascades in rotating stratified turbulence (1995) J. Atmos. Sci., 52, p. 4410
  • Ḿetais, O., Bartello, P., Garnier, E., Riley, J.J., Lesieur, M., Inverse cascade in stably stratified rotating turbulence (1996) Dyn. Atmos. Oceans, 23, p. 193
  • Kurien, S., Wingate, B., Taylor, M.A., Anisotropic constraints on energy distribution in rotating and stratified turbulence (2008) Europhys. Lett., 84, p. 24003
  • Smith, L.M., Chasnov, J.R., Waleffe, F., Crossover from two- to three-dimensional turbulence (1996) Phys. Rev. Lett., 77, p. 2467
  • Mininni, P.D., Pouquet, A., Rotating helical turbulence. I. Global evolution and spectral behavior (2010) Phys. Fluids, 22, p. 035105
  • Marino, R., Mininni, P.D., Rosenberg, D.L., Pouquet, A., Large-scale anisotropy in stably stratified rotating flows (2014) Phys. Rev. E, 90, p. 023018
  • Vallis, G.K., (2008) Atmospheric and Oceanic Fluid Dynamics, , (Cambridge University Press, Cambridge, )
  • Dritschel, D.G., McKiver, W.J., Effect of Prandtl's ratio on balance in geophysical turbulence (2015) J. Fluid Mech., 777, p. 569
  • Hanazaki, H., Linear processes in stably and unstably stratified rotating turbulence (2002) J. Fluid Mech., 465, p. 157
  • Marino, R., Mininni, P.D., Rosenberg, D., Pouquet, A., Inverse cascades in rotating stratified turbulence: Fast growth of large scales (2013) Europhys. Lett., 102, p. 44006
  • Cambon, C., Jacquin, L., Spectral approach to non-isotropic turbulence subjected to rotation (1989) J. Fluid Mech., 202, p. 295
  • Waleffe, F., The nature of triad interactions in homogeneous turbulence (1992) Phys. Fluids A, 4, p. 350
  • Waleffe, F., Inertial transfers in the helical decomposition (1993) Phys. Fluids A, 5, p. 677
  • Cambon, C., Mansour, N.N., Godeferd, F.S., Energy transfer in rotating turbulence (1997) J. Fluid Mech., 337, p. 303
  • Cambon, C., Turbulence and vortex structures in rotating and stratified flows (2001) Eur. J. Mech. - B/Fluids, 20, p. 489
  • Nikurashin, M., Vallis, G.K., Adcroft, A., Routes to energy dissipation for geostrophic flows in the Southern Ocean (2012) Nat. Geosci., 6, p. 48
  • Shih, L.H., Koseff, J.R., Ivey, G.N., Ferziger, J.H., Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations (2005) J. Fluid Mech., 525, p. 193
  • Mininni, P.D., Rosenberg, D., Pouquet, A., Isotropization at small scales of rotating helically driven turbulence (2012) J. Fluid Mech., 699, p. 263
  • Delache, A., Cambon, C., Godeferd, F., Scale by scale anisotropy in freely decaying rotating turbulence (2014) Phys. Fluids, 26, p. 025104
  • Rorai, C., Mininni, P.D., Pouquet, A., Stably stratified turbulence in the presence of large-scale forcing (2015) Phys. Rev. E, 92, p. 013003
  • Cho, J.Y.N., Zhu, Y., Newell, R.E., Anderson, B.E., Barrick, J.D., Gregory, G.L., Sachse, G.W., Albercook, G.M., Horizontal wavenumber spectra of winds, temperature, and trace gases during the Pacific Exploratory Missions: 1. Climatology (1999) J. Geophys. Res., 104, p. 5697
  • Vincent, D.G., Schlatter, T.W., Evidence of deep convection as a source of synoptic-scale kinetic energy (1979) Tellus, 31, p. 493
  • Liechtenstein, L., Godeferd, F.S., Cambon, C., Nonlinear formation of structures in rotating stratified turbulence (2005) J. Turbul., 6, p. N24
  • Billant, P., Chomaz, J.-M., Self-similarity of strongly stratified inviscid flows (2001) Phys. Fluids, 13, p. 1645
  • Babin, A., Mahalov, A., Nicolaenko, B., Zhou, Y., On the asymptotic regimes and the strongly stratified limit of rotating Boussinesq equations (1997) Theor. Comput. Fluid Dyn., 9, p. 223
  • Julien, K., Knobloch, E., Werne, J., A new class of equations for rotationally constrained flows (1998) Theor. Comput. Fluid Dyn., 11, p. 251
  • Smith, L.M., Waleffe, F., Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence (1999) Phys. Fluids, 11, p. 1608
  • Bellet, F., Godeferd, F.S., Scott, J.F., Wave turbulence in rapidly rotating flows (2006) J. Fluid Mech., 562, p. 83
  • Kafiabad, H.A., Bartello, P., Balance dynamics in rotating stratified turbulence (2016) J. Fluid Mech., 795, p. 914
  • Alexakis, A., Rotating Taylor-Green flow (2015) J. Fluid Mech., 769, p. 46
  • di Leoni, P.C., Mininni, P.D., Quantifying resonant and near-resonant interactions in rotating turbulence (2016) J. Fluid Mech., 809, p. 821
  • Smith, L.M., Lee, Y., On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number (2005) J. Fluid Mech., 535, p. 111
  • Nazarenko, S., (2011) Wave Turbulence, , (Springer, New York, )
  • Kraichnan, R.H., Inertial-range spectrum of hydromagnetic turbulence (1965) Phys. Fluids, 8, p. 1385
  • di Leoni, P.C., Cobelli, P.J., Mininni, P.D., Dmitruk, P., Matthaeus, W.H., Quantification of the strength of inertial waves in a rotating turbulent flow (2014) Phys. Fluids, 26, p. 035106
  • Chen, S., Kraichnan, R.H., Sweeping decorrelation in isotropic turbulence (1989) Phys. Fluids A, 1, p. 2019
  • Dubrulle, B., Valdettaro, L., Consequences of rotation in energetics of accretion disks (1992) Astron. Astrophys., 263, p. 387
  • Zhou, Y., A phenomenological treatment of rotating turbulence (1995) Phys. Fluids, 7, p. 2092
  • Pouquet, A., Mininni, P.D., The interplay between helicity and rotation in turbulence: Implications for scaling laws and small-scale dynamics (2010) Philos. Trans. R. Soc., A, 368, p. 1635
  • Campagne, A., Gallet, B., Moisy, F., Cortet, P.-P., Direct and inverse energy cascades in a forced rotating turbulence experiment (2014) Phys. Fluids, 26, p. 125112
  • Cambon, C., Rubinstein, R., Godeferd, F.S., Advances in wave turbulence: Rapidly rotating flows (2004) New J. Phys., 6, p. 73
  • Paret, J., Tabeling, P., Experimental observation of the two-dimensional inverse energy cascade (1997) Phys. Rev. Lett., 79, p. 4162
  • Sommeria, J., Experimental study of the two-dimensional inverse energy cascade in a square box (1986) J. Fluid Mech., 170, p. 139
  • Mininni, P.D., Alexakis, A., Pouquet, A., Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: The slow emergence of scaling laws (2008) Phys. Rev. E, 77, p. 036306
  • Marino, R., Pouquet, A., Rosenberg, D., Resolving the paradox of oceanic large-scale balance and small-scale mixing (2015) Phys. Rev. Lett., 114, p. 114504
  • Reinhaud, J.N., Dritschel, D.G., Koudella, C.R., The shape of vortices in quasi-geostrophic turbulence (2003) J. Fluid Mech., 474, p. 175
  • Herbert, C., Pouquet, A., Marino, R., Restricted equilibrium and the energy cascade in rotating and stratified flows (2014) J. Fluid Mech., 758, p. 374
  • Marino, R., Rosenberg, D., Herbert, C., Pouquet, A., Interplay of waves and eddies in rotating stratified turbulence and the link with kinetic-potential energy partition (2015) Europhys. Lett., 112, p. 49001
  • di Leoni, P.C., Cobelli, P.J., Mininni, P.D., The spatio-temporal spectrum of turbulent flows (2015) Eur. Phys. J. E, 38, p. 1
  • Yarom, E., Sharon, E., Experimental observation of steady inertialwave turbulence in deep rotating flows (2014) Nat. Phys., 10, p. 510
  • Campagne, A., Gallet, B., Moisy, F., Cortet, P.-P., Disentangling inertial waves from eddy turbulence in a forced rotating-turbulence experiment (2015) Phys. Rev. E, 91, p. 043016
  • Sagaut, P., Cambon, C., (2008) Homogeneous Turbulence Dynamics, , (Cambridge University Press, Cambridge,)
  • Miquel, B., Mordant, N., Nonlinear dynamics of flexural wave turbulence (2011) Phys. Rev. E, 84, p. 066607
  • Greenspan, H., (1968) The Theory of Rotating Fluids, , (Cambridge University Press, Cambridge, )

Citas:

---------- APA ----------
Oks, D., Mininni, P.D., Marino, R. & Pouquet, A. (2017) . Inverse cascades and resonant triads in rotating and stratified turbulence. Physics of Fluids, 29(11).
http://dx.doi.org/10.1063/1.5001740
---------- CHICAGO ----------
Oks, D., Mininni, P.D., Marino, R., Pouquet, A. "Inverse cascades and resonant triads in rotating and stratified turbulence" . Physics of Fluids 29, no. 11 (2017).
http://dx.doi.org/10.1063/1.5001740
---------- MLA ----------
Oks, D., Mininni, P.D., Marino, R., Pouquet, A. "Inverse cascades and resonant triads in rotating and stratified turbulence" . Physics of Fluids, vol. 29, no. 11, 2017.
http://dx.doi.org/10.1063/1.5001740
---------- VANCOUVER ----------
Oks, D., Mininni, P.D., Marino, R., Pouquet, A. Inverse cascades and resonant triads in rotating and stratified turbulence. Phys. Fluids. 2017;29(11).
http://dx.doi.org/10.1063/1.5001740